Gradient Reverse:
Assumed the speaker information \(u\)  is
related to timbre \({Z}_{t}\)  only, while independent of rhyme \({Z}_{r}\) , pitch \({Z}_{p}\)  and content \({Z}_{c}\) .
First, we aim to disentangle speaker-irrelevant information \(\lbrace {Z}_{r}, {Z}_{p}, {Z}_{c}\rbrace \)  from speaker relevant timber \({Z}_{t}\) .
Instead of directly minimizing \(\mathcal {I}(\lbrace {Z}_{r}, {Z}_{p}, {Z}_{c}\rbrace , {Z}_{t})\) , we can maximize \(\mathcal {I}({Z}_{t}, u)\) 
and minimize \(\mathcal {I}(\lbrace {Z}_{r}, {Z}_{p}, {Z}_{c}\rbrace , u)\)  respectively,
which can be implemented as common classifier \(C_1\)  and adversarial speaker classifier \(C_2\) .
As shown in Fig.REF , the input of \(C_1\)  is \({Z}_{t}\)  and the input of \(C_2\)  is \(\lbrace {Z}_{r}, {Z}_{p}, {Z}_{c}\rbrace \) .
GRL [1]} is inserted in \(C_2\)  as the adversarial classifier.
The two classifiers can be formulated as:
\(\begin{split}\mathcal {L}_{\text{com-cls}}\left({\theta }_{e_{c_{1}}}, {\theta }_{c_{1}}\right)&=-\sum _{k=1}^{K} \mathbb {I}(u==k) \log p_{k}^{\prime } \\\mathcal {L}_{\text{adv-cls }}\left({\theta }_{e_{c_{2}}}, {\theta }_{c_{2}}\right)&=-\sum _{k=1}^{K} \mathbb {I}(u==k) \log p_{k}\end{split}\) 
